Turbulent flow drag reduction

ABSTRACT

The present invention relates to apparatus for influencing fluid flow over a surface, and more particularly, but not exclusively, to turbulent boundary layer flow drag reduction for an aircraft. The present invention provides such apparatus including a plasma generator comprising a first electrode and a signal generator, the apparatus being operable to drive the first electrode with a pulsed signal generated by the signal generator thereby to cause a change in direction of the flow of the fluid over the surface.

This application is the US national phase of international applicationPCT/GB02/01449 filed 26 Mar. 2002, which designated the US.PCT/IB02/01449 claims priority of GB Application No. 0108738.6 filed 06Apr. 2001. The entire contents of these applications are incorporatedherein by reference.

The present invention relates to apparatus for influencing fluid flowover a surface, and more particularly, but not exclusively, to turbulentboundary layer flow drag reduction for an aircraft.

The boundary layer is a thin layer of fluid (air) that forms, forexample, on an aircraft wing during flight adjacent to the surface ofthe wing in which viscous forces exert an influence on the motion of thefluid and in which the transition between still air and the wing'svelocity occurs. Boundary layer control techniques are known where theairflow in the boundary layer is modified to increase and/or decreasedrag.

Turbulent boundary layer flow is not yet fully understood, but therecognition that coherent structures exist has allowed efforts to bedirected to modifying and/or controlling the turbulent boundary layerflow, as described, for example, in AIAA paper 96-0001—“Control ofTurbulence”—J. Lumley. Direct numerical simulation of the turbulentboundary layer flow, as described, for example in Phys. Fluids A 4(8)—“Suppression of Turbulence in Wall-bounded Flows by High FrequencySpanwise Oscillations”—W. J. Jung, N. Mangiavacchi, R. Akhavan showsthat disrupting the coherent structures could have a dramatic effect onthe skin friction, reducing it by up to 40%. If this level could beachieved on an aircraft this would equate to a reduction in total dragof between 10% and 20% offering substantial savings in fuel and/orincreases in range. Experimental verification of this numericalprediction has been achieved and published in AIAA paper97-1795—“Turbulent Boundary Layer Control by means of Spanwise-wallOscillation”—K-S. Choi, P. E. Roach, J-R. DeBisschop, and B. R. Clayton.In that paper the use of mechanical oscillation is described todemonstrate skin friction reductions of up to 45%. However, the paperdoes not suggest how a practical mechanical oscillation system could beimplemented successfully.

Other approaches for actively disrupting the coherent structures, suchas blowing, or using tiny micro-electro-mechanical actuators have beenpostulated, but no practical and effective means have been demonstrated.Passive modification of the coherent flow structures has also beenattempted, for example, riblets and large eddy break-up devices. Theseapproaches have achieved skin friction drag reductions, but at a muchsmaller level (less than 10% as opposed to 40%) and are thereforemarginal in their overall benefits once extra cost and other penalties(such as increased weight) are considered.

There remains a need for a passive or active system that disrupts thecoherent turbulent boundary layer structures to achieve large skinfriction reductions, which is both practical and cost effective. In the1998 conference publication AIAA 36th Aerospaces Meeting, paper AIAA98-0328—“Boundary Layer Control with a One Atmosphere Uniform GlowDischarge Surface Plasma”—Reece-Roth, Sherman and Wilkinson, anelectrode system based on rigid printed circuit board material isdescribed and the interaction of surface plasmas with boundary layersrelated. The electrode system comprises a single set of a multiplicityof parallel conductive lines all electrically connected to one another.The plasma generating circuit is a high voltage radio frequency sourceoperated at 3.0 kHz. The interaction of the surface plasmas with theairflow was said in this paper to be due to an electrostatic attractiveforce—termed paraelectric. At the end of the paper it is postulated thatthis sort of technology might be applicable to the generation ofspan-wise oscillations for turbulent drag reduction. No information onhow this concept could be achieved was given.

Both travelling wave and span-wise oscillation boundary layerdisturbances have been tried for drag reduction in sea water (using acombination of magnetic and electric field forces). Travelling waveshave been found to be more effective, at least under certain conditions,as described in Science 288, 1230 (2000)—“Suppressing Wall Turbulence byMeans of a Transverse Traveling Wave”, Du and Karniadakis.

It is an object of the present invention to provide an arrangement forinfluencing fluid flow so that an object's drag can be reduced.

According to a first aspect of the present invention, there is providedapparatus for influencing fluid flow over a surface, the apparatusincluding a plasma generator comprising a first electrode and a signalgenerator, the apparatus being operable to drive the first electrodewith a pulsed signal generated by the signal generator thereby to causea change in direction of the flow of the fluid over the surface. Byproviding a pulsed signal, plasma is generated in a number of discretesteps such that fluid is caused to flow over the surface by the fluidbeing given intermittent ‘kicks’ to keep the fluid moving.

The pulsed signal may comprise a pulse envelope containing a varyingsignal which may, optionally, comprise a train of shorter durationpulses. Advantageously, the pulse envelope may contain 10 to 100 pulses.Conveniently, the pulse envelope duration and the pulse enveloperepetition period may be independently adjustable.

Optionally, the plasma generator is operable to cause a change indirection of the flow of the fluid over the surface primarily in asingle direction. To this end, the first electrode may comprise firstand second elongate elements which may be in juxtaposed and, optionally,substantially parallel alignment. Advantageously, the first and secondelongate elements extend generally parallel to the usual direction ofmotion of the surface in use. Optionally, the apparatus is operable suchthat first elongate element receives a first pulse and the secondelongate element receives a second pulse after a time interval at leastas long as the time taken for fluid to travel between the first andsecond elongate elements. Advantageously, the apparatus is operable todrive the first and second elongate elements with a common pulsed signalgenerated by the signal generator, the period of the pulsed signal beingat least as long as the time taken for fluid to travel between the firstand second elongate elements. In this way, the fluid may be repeatedly‘kicked’ in a common direction.

Optionally, the plasma generator is operable to cause a change indirection of the flow of the fluid over the surface in alternategenerally opposite directions. The plasma generator may further comprisea second electrode operable independently of the first electrode inresponse to a pulsed signal generated by the signal generator. Providingfirst and second independently controllable electrodes provides fargreater flexibility of operation over the prior art system of providinga single set of a multiplicity of parallel conductive lines allelectrically connected to one another. For example, the plasma generatormay be operable to cause the fluid to flow in alternate generallyopposite directions along the surface. In this way, spanwiseoscillations may be created. If these generally opposite directions aregenerally perpendicular to the principal direction of fluid flow overthe surface (caused, for example, by movement of the surface through thefluid), this may tend to reduce drag.

Conveniently, the first and second electrodes are in juxtaposedalignment and may, optionally, be in substantially parallel alignment.Advantageously, the first and second electrodes extend generallyparallel to the usual direction of motion of the surface in use.

Optionally, the signal generator is operable to supply pulses to thefirst and second electrodes alternately thereby driving the first andsecond electrodes alternately. There are two currently preferred modesof operation of this type. In the first mode, pulses are used to drivefirst and second electrodes spaced apart over a time interval slightlylonger than the time taken for fluid to travel between the first andsecond electrodes. In this way, the fluid is repeatedly kicked in acommon direction, akin to the mode described above for a first electrodecomprising first and second electrodes. In the second mode, pulses areused to drive first and second electrodes spaced apart over a timeinterval slightly shorter than the time taken for fluid to travelbetween the first and second electrodes. In this way, the fluid iskicked back in the opposite direction as it approaches the secondelectrode from the first electrode. If this is repeated, the fluid isrepeatedly kicked from one electrode to the other and spanwiseoscillations can be obtained.

Optionally, the plasma generator includes a dielectric that supports thefirst electrode and any second electrode on a first side thereof.Electrodes may be formed on surfaces of the dielectric layer or could bewithin the dielectric layer. Conveniently, the dielectric may be in theform of a flexible sheet so that it may be attached to curved surfacessuch as an aircraft wing. Optionally, the dielectric comprises a secondside that supports an opposed electrode of the plasma generator, thefirst and second sides being generally opposed.

The first and second electrodes may comprise a plurality of electricallyconnected elongate elements which may be arranged such that the elongateelements are interdigitated. Conveniently, the opposed electrode maycomprise a plurality of electrically connected elongate elements. Theelongate elements of the first, second and opposed electrodes may be ina substantially parallel juxtaposed alignment when viewed facing thefirst side of the dielectric. Advantageously, the elongate elements ofthe first, second and opposed electrodes may extend substantiallyparallel to the usual direction of motion of the surface. The elongateelements of the opposed electrode may be laterally offset from theelongate elements of the first and second electrodes.

The present invention also relates to an aircraft aerodynamic surfaceand an aircraft including apparatus as defined above, wherein the plasmagenerator is operable to cause a change in direction of the flow of thefluid over the surface.

According to a second aspect of the present invention, there is provideda method of influencing fluid flow over a surface, comprising the stepof driving an electrode provided on the surface with a pulsed signalthereby to generate a plasma and, in turn, to cause a change indirection of the flow of the fluid over the surface.

For a better understanding of the present invention, embodiments willnow be described, by way of example, with reference to the accompanyingdrawings, in which:

FIG. 1 shows an aircraft wing on which an electrode arrangement inaccordance with the present invention is formed;

FIG. 2 is a schematic diagram of the apparatus for generating a plasma;

FIG. 3 shows the timing of the pulses applied to the electrodes;

FIG. 4 shows in more detail the waveform of the pulses applied to theelectrodes; and

FIGS. 5A and B show an alternative embodiment of the plasma generatingapparatus in perspective and cross-section, respectively.

In the drawings, like elements are generally designated with the samereference numerals.

FIG. 1 shows a wing model 1 to which an electrode assembly 3 inaccordance with the present invention is attached. The leading edge ofthe wing 1 is designated 5.

The electrode assembly 3 comprises first and second electrodes 7 and 9.

The electrodes 7 and 9 are similar in shape, and have a generallycomb-like structure. Each electrode 7 and 9 comprises a plurality ofparallel, vertically extending (in FIG. 1) fingers which are connectedby a horizontal (in FIG. 1) strip. The fingers and the strip of eachelectrode 7 and 9 are integrally formed with one another. The firstelectrode 7 has a terminal 11 for connection to a power supply andsecond electrode 9 has a terminal 13 for connection to a power supply.

In the drawings only a limited number of electrode “fingers” are shown,for the sake of clarity. It will be understood that many more fingerswould be employed in an electrode assembly for a commercial aircraft.

The first 7 and second 9 electrodes are interdigitated. As shown in FIG.2, the electrodes 7 and 9 are formed on a sheet 15 of dielectricmaterial, such as a polyester sheet which, in the embodiment, is 250 μmthick. A third, planar sheet electrode 16 is formed on the opposite sideof the dielectric layer 15 to the first and second electrodes 7 and 9.The first, second and third electrodes 7, 9 and 16 are formed fromcopper and are 17 μm thick. The first and second electrodes 7 and 9 areformed by a conventional etching process. The fingers of each of thefirst and second electrodes 7 and 9 are between 200 μm and 500 μm wide,with each finger being spaced apart from its adjacent finger by 4 mm(adjacent fingers will be of different electrodes).

The first, second and third electrodes 7, 9 and 16 are driven byalternating current high-tension power supply 18.

The electrode assembly 3, comprising the three electrodes 7, 9 and 16and the dielectric layer 15, is formed as a flexible sheet. Theelectrode assembly 3 can be adhered to a surface where it is required,such as an aircraft wing or fuselage. The flexibility of the sheetallows the electrode assembly 3 to be attached to curved surfaces, andthe electrode assembly 3 is retro-fittable to existing aircraft withminimal structural disruption.

If the aircraft wing, or the structure to which the electrode assembly 3is attached, is of metal or other electrically conductive material, thethird electrode 16 may not be formed, and the conductive structure maybe used to provide the function of that electrode by connecting theconductive structure to the power supply 18.

The power supply 18 is configured to alternately drive at the desiredspan-wise oscillation frequency first electrode 7 and second electrode9.

FIG. 3 shows the duration and timing of the electrical pulses applied toterminals 11 and 13 of the first 7 and second 9 electrodes respectively.The upper oscillation current pulses shown in the Figure are applied tofirst electrode 7 and the lower oscillation current pulses are appliedto second electrode 9. As can be seen, a pulse is never applied to thefirst 7 and second 9 electrodes at the same time. Each pulse envelope 20comprises a plurality of shorter duration plasma pulses 22.

The signals have a pulse envelope repetition period T, determining thespan-wise oscillation frequency. The Jung paper “Suppression ofTurbulence in Wall-bounded Flows by High Frequency Spanwise Oscillation”referred to above describes how to select a span-wise oscillationfrequency range that will reduce drag. Periods of oscillation T⁺ _(osc)ranging from 25 to 200 were studied, whereT ⁺ _(osc) =T _(osc.) U _(τ) ²/ν

-   -   T_(osc) being the oscillation period of the wall    -   U_(τ) being the wall friction velocity    -   ν being kinematic viscosity.

It was found that T⁺ _(osc)=100 produced the most effective suppressionof turbulence.

Within each pulse envelope 20 of the signal is a train of highrepetition-rate pulses 22, for example 10 to 100 pulses. FIG. 4 shows inmore detail the voltage waveform 24 and the current waveform 26 of onepulse 22. The number of pulses 22 within each pulse envelope 20 and theenergy of these pulses can be varied to allow adjustment of the impulseimparted to the air in the boundary layer. Generally, the greater thenumber and the energy of the pulses 20, the greater the effect on theboundary air. However, increasing the number of pulses, and the energyof each pulse will result in increased power consumption. Since, whenimplemented on an aircraft wing, the device is intended to allow areduction in fuel consumption of the aircraft engines, there will be nooverall saving in energy consumption if the power consumed by the plasmagenerating apparatus equals the energy saved by the reduction in drag.The energy applied to the pulse generating apparatus should be chosen toreduce the overall energy consumption of the aircraft in flight.

The duration D of the pulse envelope and the pulse envelope repetitionperiod T can be independently adjusted.

Plasma is initiated by the high electric field at the first 7 and second9 electrode/dielectric 15/air triple point 27, and then spreads out,capacitively coupled, to the third, planar electrode 16 on the oppositeside of the dielectric layer 15 to the first and second electrodes 7 and9. The electrode assembly 3 has an inherent capacitance, and additionalcapacitance when the plasma is formed.

The plasma generates span-wise impulses 28 in the boundary layer at thespan-wise oscillation frequency. The impulses 28 are created by theplasma heating and causing expansion of the air in the boundary layeradjacent to the first 7 and second 9 electrodes. The impulses 28 move ina span-wise direction, which is generally perpendicular to the direction30 of the primary airflow over the aircraft wing 1. It is considered bythe present inventors that generating impulses generally perpendicular(within ±10°) to the principal direction 30 of airflow reduces drag.

Airflow is generated in a span-wise oscillating fashion because adjacentelectrodes 7 and 9 are alternatively driven. When the first electrode 7is driven, as mentioned above, the application of power to the electrodecauses the heating and expansion of the air adjacent to the electrode 7.The expanding air will radiate from the electrodes, with components ofthe expanding air moving in opposite span-wise directions. During theperiod L when no pulses are applied to any of the electrodes the fluidwill continue to flow. When the second electrode 9 is driven the airadjacent to this electrode 9 will also be heated and expand. Thisexpansion will serve to reverse the span-wise movement of the air causedby the previous pulse supplied to the first electrode 7. The repeatedalternate application of pulses to the electrode 7 and 9 thereforecauses span-wise oscillation of air adjacent to electrodes 7 and 9 onthe wing 1 surface. A suitable oscillation frequency range is thought tobe between 10⁴ and 10⁵ Hz. The value will be chosen according to thelocation of the electrode assembly 3 on the aircraft and the speed ofthe aircraft.

In the embodiment the plasma spreads out approximately 4 mm on eitherside of each of the electrode fingers when a peak voltage ofapproximately 4 kV is applied.

The power supply 18 may generate a semiconductor switched current pulsewhich is already at a sufficiently high voltage for plasma generation,or, if not, the pulse is fired into a step-up transformer. Fornon-resonant charging of the electrode assembly 3 the output can betaken through a charging resistor. Resonant charging can also be usedfrom a supply with no charging resistor. Current flows and when a plasmageneration threshold is exceeded, plasma is generated therebydissipating power. In the present embodiment, when a sheet 15 of 250 μmthick polyester is used for the dielectric material, the plasmageneration threshold will be approximately 2 kV. Integrating the voltageand current waveforms shows the energy balance—this rises as thestructure charges and then drops as it discharges but not by as much asit rose, the difference is the energy dissipated in the plasma.Multiplying by the plasma pulse repetition rate and the duty cycle givesthe average power dissipation. Dividing by the electrode sheet surfacearea gives the power per unit area. This is an important factor—in orderfor drag reduction to be efficient, the power per unit area must be lessthan the power drag reduction of the skin friction. Pulses of bothpolarities are used for plasma generation.

In the embodiment the pulse rise time is short compared to the pulseperiod. Typical energy dissipations per centimeter of electrode lengthper pulse at 4 kV are approximately 30 μJ. There can be differencesbetween positive and negative polarities but this is an approximatefigure. It is estimated that air velocities of >1 ms⁻¹ can be generatedwithin a few millimeters of the first and second electrodes 7 and 9 andclose to the surface of the dielectric layer 15.

FIGS. 5A and 5B show an alternative arrangement where only a singleelectrode 32 is provided on the upper (in FIG. 5) surface of thedielectric layer 15. On the lower (in FIG. 5) surface of the dielectriclayer 15 a further electrode 34 is formed. The upper electrode 32 iscomb-like and is similar in configuration to either of the first 7 orsecond 9 electrodes of the first embodiment. The lower electrode 34 isof a similar configuration to the upper electrode 32 but is laterallyoffset with respect to the upper electrode 32, as shown particularly inthe cross-sectional view of FIG. 5B. Because the electrodes 32 and 34are offset, the plasma generated is generally confined to one side 36 ofthe electrode 32. Because the plasma is generated to only one side ofthe electrode 32 this will cause heating and expansion of the airgenerally in a single direction 38.

In this embodiment, if the aircraft wing, or the structure to which theelectrode assembly 3 is attached, is of metal or other electricallyconductive material, an insulator should be provided between the lowerelectrode 34 and conductive structure.

The electrode 32 is driven with a signal having a configuration of oneof the waveforms shown in FIG. 3, i.e. a periodically repeating pulseenvelope 20 containing a series of high frequency pulses 22. The timingof the pulse envelopes 20 is selected so that the distance D travelledby the air driven by a first pulse envelope is equal to or greater thanthe distance d between adjacent fingers of the electrode 32. Therefore,air moved as a result of plasma generation by first electrode finger32.1 will have flowed in a span-wise direction to or past electrodefinger 32.2 when the subsequent pulse is applied. The subsequent pulsewill push this air further in the direction 38, thus continuing the flowin a single span-wise direction along the wing.

By timing the pulse envelope repetition period T so that it coincideswith the air impulse transit time a coherent boundary layer travellingwave is generated which will disrupt turbulent flow structures.

Although in the first embodiment the air oscillates in oppositespan-wise direction, and in the second embodiment the air travels in asingle span-wise direction, in both the embodiments it will understoodthe movement of the air generated by the plasma generating apparatus isgenerally perpendicular to the direction 30 of the main airflow.

The plasma generating apparatus may be controlled so that it does notoperate during take-off and landing of the aircraft, and generally atlow altitudes. It may be advantageous not to operate the plasmagenerating apparatus in these situations for safety reasons—operationmay interfere with electronic apparatus in the aircraft and also on theground, at the airport.

1. Apparatus for influencing boundary layer fluid flow over a surface,the apparatus including a plasma generator comprising: a firstelectrode, said first electrode comprising first and second elongateelements; and a signal generator for driving the first electrode with apulsed signal and for causing said fluid to move in a direction from oneof said elongate elements to the other of said elongate elements,wherein said first elongate element receives a first pulse and thesecond elongate element receives a second pulse after a time interval atleast as long as the time taken for fluid to travel between the firstand second elongate elements.
 2. Apparatus according to claim 1, whereinthe pulsed signal comprises a pulse envelope containing a varyingsignal.
 3. Apparatus according to claim 2, wherein the pulse envelopecontains a train of shorter duration pulses.
 4. Apparatus according toclaim 3, wherein the pulse envelope contains 10 to 100 pulses. 5.Apparatus according to claim 2, wherein the pulse envelope duration andthe pulse envelope repetition period are independently adjustable. 6.Apparatus according to claim 1, wherein the plasma generator is operableto cause a change in direction of the flow of the fluid over the surfaceprimarily in a single direction.
 7. Apparatus according to claim 1,wherein the first and second elongate elements are in juxtaposedalignment.
 8. Apparatus according to claim 7, wherein the first andsecond elongate elements are in substantially parallel alignment. 9.Apparatus according to claim 8, wherein the first and second elongateelements extend generally parallel to the usual direction of motion ofthe surface in use.
 10. Apparatus according to claim 1, wherein theapparatus is operable such that first elongate element receives a firstpulse and the second elongate element receives a second pulse after atime interval at least as long as the time taken for fluid to travelbetween the first and second elongate elements.
 11. Apparatus accordingto claim 10, wherein the apparatus is operable to drive the first andsecond elongate elements with a common pulsed signal generated by thesignal generator, the period of the pulsed signal being at least as longas the time taken for fluid to travel between the first and secondelongate elements.
 12. Apparatus according to claim 1, wherein theplasma generator is operable to cause a change in direction of the flowof the fluid over the surface in alternate generally oppositedirections.
 13. Apparatus according to claim 12, wherein the plasmagenerator further comprises a second electrode operable independently ofthe first electrode in response to a pulsed signal generated by thesignal generator.
 14. Apparatus according to claim 13, wherein the firstand second electrodes are in juxtaposed alignment.
 15. Apparatusaccording to claim 14, wherein the first and second electrodes are insubstantially parallel alignment.
 16. Apparatus according to claim 15,wherein the first and second electrodes extend generally parallel to theusual direction of motion of the surface in use.
 17. Apparatus accordingto claim 12, wherein the signal generator is operable to supply pulsesto the first and second electrodes alternately thereby driving the firstand second electrodes alternately.
 18. Apparatus according to claim 17,wherein the apparatus is operable such that first electrode receives afirst pulse and the second electrode receives a second pulse after atime interval less than the time taken for fluid to travel between thefirst and second electrodes.
 19. Apparatus according to claim 1, whereinthe plasma generator includes a dielectric that supports the firstelectrode and any second electrode on a first side thereof. 20.Apparatus according to claim 19, wherein the dielectric is in the formof a flexible sheet.
 21. Apparatus according to claim 19, wherein thedielectric comprises a second side that supports an opposed electrode ofthe plasma generator, the first and second sides being generallyopposed.
 22. Apparatus according to claim 13, wherein each of the firstand second electrodes comprise a plurality of electrically connectedelongate elements.
 23. Apparatus according to claim 22, wherein thefirst and second electrodes are arranged such that the elongate elementsare interdigitated.
 24. Apparatus according to claim 23, wherein theopposed electrode comprises a plurality of electrically connectedelongate elements.
 25. Apparatus according to claim 24, wherein theelongate elements of the first, second and opposed electrodes are in asubstantially parallel juxtaposed alignment when viewed facing the firstside of the dielectric.
 26. Apparatus according to claim 25, wherein theelongate elements of the first, second and opposed electrodes extendsubstantially parallel to the usual direction of motion of the surface.27. Apparatus according to claim 25, wherein the elongate elements ofthe opposed electrode are laterally offset from the elongate elements ofthe first and second electrodes.
 28. An aircraft aerodynamic surfaceincluding apparatus according to claim 1, wherein the plasma generatoris operable to cause a change in direction of the flow of the fluid overthe surface.
 29. An aircraft including apparatus according to claim 1,wherein the plasma generator is operable to cause a change in directionof the flow of the fluid over the surface.